Separation of doping density and minority carrier lifetime in photoluminescence measurements on semiconductor materials

ABSTRACT

Methods are presented for separating the effects of background doping density and effective minority carrier lifetime on photoluminescence (PL) generated from semiconductor materials. In one embodiment the background doping density is measured by another technique, enabling PL measurements to be analysed in terms of effective minority carrier lifetime. In another embodiment the effective lifetime is measured by another technique, enabling PL measurements to be analysed in terms of background doping density. In yet another embodiment, the effect of background doping density is removed by calculating intensity ratios of two PL measurements obtained in different spectral regions, or generated by different excitation wavelengths. The methods are particularly useful for bulk samples such as bricks or ingots of silicon, where information can be obtained over a much wider range of bulk lifetime values than is possible with thin, surface-limited samples such as silicon wafers. The methods may find application in solar cell manufacturing for improving the manufacture of silicon ingots and bricks, or for providing a cutting guide for wafering.

FIELD OF THE INVENTION

The present invention relates to the characterisation of semiconductormaterials using photoluminescence measurements, and in particular totechniques for separating the effects of doping density and minoritycarrier lifetime on the photoluminescence signal. The invention has beendeveloped primarily for the characterisation of bulk (i.e. non-wafer)silicon samples, however it will be appreciated that the invention isnot limited to this particular field of use.

BACKGROUND OF THE INVENTION

Commercial wafer based solar cells are made from typically 10×10 cm² upto 22×22 cm² silicon wafers. As illustrated in FIG. 1, a castmulticrystalline silicon block 2 (also known as an ingot), typically1×1×0.7 m³ in size, is sawn into square (10×10 cm² up to 22×22 cm²)shaped columns 4 (commonly known as bricks), which are then sawn intoindividual wafers 6, each typically 120-250 μm thick. An ingot isusually sawn into 4×4 or 5×5 bricks. Solar cells can be made frommulticrystalline silicon or monocrystalline silicon, with differenttechniques used for growing multicrystalline and monocrystalline siliconingots.

For wafer manufacturers it is of interest to characterise the electronicand structural properties of ingots or bricks prior to wafer slicing. Itis commonly known that cast multicrystalline (mc) silicon ingots haveincreased impurity concentration within the silicon in the outsideregions of the ingot, i.e. at the bottom, top and sides. At the bottomand the sides this is the result of diffusion of impurities from thecrucible walls into the ingot, while at the top it is caused bysegregation of impurities towards the upward-moving top liquid phaseduring crystallisation of the ingot. A result of the increased impurityconcentration is reduced electronic material quality, described by alower effective minority carrier lifetime. FIG. 2 shows in side view atypical effective minority carrier lifetime distribution in a cast mcsilicon ingot, showing an area of mostly high effective lifetimematerial 8 in the centre and regions of low lifetime 10 at the top,bottom and sides.

Experimental techniques that are currently in use for characterisationof bricks include infrared (IR) transmission and minority carrierlifetime scanning. In the former technique, the transmission of sub-bandgap light through the brick is measured from different directions withan IR camera that is sensitive to the sub band-gap spectral range(wavelengths>1100 nm for silicon), providing three-dimensionalinformation about the density and position of inclusions such as siliconcarbide (SiC) and silicon nitride (Si₃N₄).

Several experimental techniques exist for measuring the effectiveminority carrier lifetime, including both transient and quasi steadystate photoconductance (QSSPC) and microwave photoconductance decay(μ-PCD). These techniques measure the effective minority carrierlifetime, which is an effective sample characteristic parameter affectedby both the bulk material quality (i.e. the bulk minority carrierlifetime) and surface recombination. Especially on samples withunpassivated surfaces, such as as-cut wafers, the effective lifetime isusually strongly affected or dominated by surface recombination.Two-dimensional information about lateral variations of the effectivelifetime, e.g. on one surface of a brick, can be obtained by using theabove methods in a scanning mode, generating a map via point by pointscanning in a manual or automated fashion. In some cases, such as QSSPC,the measured effective lifetime data can be converted into bulk lifetimedata over a limited range by using predetermined relationships betweenbulk lifetime and effective lifetime.

Although the effective minority carrier lifetime is the more easilymeasured quantity, the bulk minority carrier lifetime is the moreimportant quantity for photovoltaic applications because: (a) the impactof surface recombination is significantly reduced in subsequentprocessing via removal of low lifetime surface material and surfacepassivation; and (b) bulk lifetime, unlike effective lifetime on anunpassivated sample, determines both the voltage and the current of afinished solar cell. Especially for unpassivated samples with highsurface recombination, it is therefore important to be able to convertan as-measured effective lifetime to bulk lifetime.

Another important aspect of minority carrier lifetime is its dependenceon the injection level. The bulk lifetime is determined by variousrecombination mechanisms, including defect recombination, radiativerecombination and Auger recombination. The recombination rate via thesemechanisms is non-linear in the concentration of minority carriers andas a result the bulk minority carrier lifetime itself depends on thedensity of minority carriers. Ideally therefore, experimental data forthe minority carrier lifetime should be reported as a function ofinjection level, whether lifetime is area-averaged or spatiallyresolved. However, since representation of data as a function of twoindependent parameters (position and injection level) is difficult,spatially resolved data such as lifetime images or lifetime maps areoften reported only for a single injection level for each point.

Upgraded Metallurgical Grade (UMG) silicon is a prospective material forachieving significant cost reductions in silicon wafer-basedphotovoltaics. A commonly observed feature of UMG ingots and bricks isan inversion of the background doping density that occurs from thebottom to the top of an ingot, caused by the presence of significantquantities (densities) of both phosphorous and boron in the feedstock.Due to the different segregation coefficients of these dopants, theirincorporation into the crystal occurs at different rates. As a resultUMG ingots are generally found to be p-type at the bottom and n-type atthe top, with a so called ‘compensated region’ in between that iseffectively undoped or only very lightly doped. A method to gaininformation quickly about the position and shape of the transitionregion is required, since wafers from that region and the n-type wafersfrom above that region cannot be used in conventional screen printedsolar cell production lines, which normally use p-type wafers.

The ability to measure the effective lifetime of silicon wafers usingphotoluminescence (PL) imaging has been described in published PCTpatent application No WO 2007/041758 A1 entitled ‘Method and System forInspecting Indirect Bandgap Semiconductor Structure’ and incorporatedherein by reference. The measurable luminescence intensity in PL imagingon semiconductor materials is determined by the rate of spontaneousemission r_(sp), which can generally be assumed to be linear in theproduct of the electron (n) and hole (p) concentrations, i.e.r_(sp)=B*n*p, where B is a proportionality factor referred to in theliterature as the radiative recombination coefficient. In PL imagingapplications on silicon samples, particularly on unpassivated surfaces,the condition of low level injection is generally fulfilled, which meansthat the excess minority carrier concentration Δn is significantlysmaller than the background doping concentration N_(d), i.e. Δn<<N_(d).In this case the total minority carrier density is given to very goodapproximation by Δn and the majority carrier density by N_(d). As aresult the emitted luminescence is proportional to the excess minoritycarrier density and the background doping density so thatr_(sp)=B*Δn*N_(d). Under quasi steady state conditions, i.e. where thegeneration and recombination rates are equal, the effective minoritycarrier lifetime is inversely proportional to the generation rate G andproportional to the minority carrier density such that τ_(eff)=Δn/G,which results in r_(sp)=B*G*τ_(eff)*N_(d). The rate of spontaneousemission and thereby the PL intensity under specific illuminationintensity (i.e. for given G) is thus proportional to the product of theeffective minority carrier lifetime and the doping density.

In previous PL imaging applications the influence of the doping densityon PL intensities has been described, but an implicit assumption oflaterally constant background doping density over the sample area wasmade. For example in T. Trupke, R. A. Bardos and J. Nyhus,‘Photoluminescence characterisation of silicon wafers and silicon solarcells’, 18th Workshop on Crystalline Silicon Solar Cells & Modules 2008,Vail, USA, the influence of the background doping density on theabsolute luminescence intensity between different samples and its impacton the calibration of PL images has been discussed. For many commonlyused silicon wafers (e.g. conventional cast mc wafers) the assumptionthat the background doping density is constant laterally across thesample area is well justified, allowing interpretation of PL images interms of lateral variations of the excess minority carrier density Δn inall cases where the surface properties of the sample (texturing andantireflection coating) are sufficiently homogeneous.

However there are several types of sample where the assumption of alaterally constant background doping density is not justified. Theseinclude:

(i) Side facets of common mc silicon bricks or ingots. Doping densityvariations N_(D)(x) within typical mc silicon bricks and ingots canoften be significant. In many cases the variation of the doping densityalong the growth direction can be described by the Scheil equation whichis derived from considering the thermodynamic potential of the dopant inthe two phases of the solidifying silicon casting block:

N _(D)(x)=N _(D)(0)·K _(eff)(1−x)^(K) ^(eff) ⁻¹

In this equation K_(eff) is a coefficient characteristic of the dominantdopant atom and the crystal host and x is the relative height within thebrick or ingot (x=0 corresponds to the bottom, x=1 to the top). Forexample for a typical 25 cm high boron doped (p-type) silicon ingot orbrick, the doping density increases by typically 30%-40% relative fromthe bottom to the top.

(ii) Side facets of UMG silicon bricks or otherwise intentionally orunintentionally doping-compensated ingots or bricks. Strong variationsof the effective doping density are observed, with a transition regionfrom effective p-type doping to n-type doping.

(iii) Wafers from UMG bricks. The transition region from p-type ton-type is not strictly parallel to the direction in which wafers are cutfrom the ingot, because of a typically curved solid-liquid interfacenear the crystallisation front. Wafers from near the transition regionwill therefore show strong variations in the doping density within eachwafer, some of them even showing a transition from p-type to n-typewithin a single wafer.

(iv) Vertical samples from Czochralsky (Cz) grown monocrystallineingots. Vertical variations in the background doping density will showup on PL images taken on silicon ingots or wafers cut vertically fromsuch ingots.

(v) Monocrystalline wafers, particularly n-type Cz wafers, often exhibitcircular variations (striations) in the doping density. These can beseen particularly clearly in luminescence images taken on unpassivatedwafers, since the effective lifetime is surface limited and thus almostconstant across the wafer area. Even small variations in doping densityare therefore clearly visible in luminescence images.

(vi) There are various other new and more exotic types of silicon ingotmanufacturing processes in development that may become mainstream.Examples include BP Solar's cast ‘mono-crystalline’ process and Muto'sdirect chemical formation process. Each new process for makingcrystalline silicon blocks will have idiosyncrasies in dopantconcentrations and lifetime variations.

Where a constant background doping density can no longer be assumed, theintensity variation in a PL image is determined by the product of 1) thedoping density and 2) the effective minority carrier lifetime. To getreliable information about spatial variations of one of these twoquantities, the PL signal therefore needs to be corrected or normalisedfor absolute or relative variations of the other quantity, which can bemeasured directly or inferred.

SUMMARY OF THE INVENTION

It is an object of the present invention to overcome or ameliorate atleast one of the disadvantages of the prior art, or to provide a usefulalternative. It is an object of the present invention in its preferredform to provide improved methods for characterising semiconductormaterials, and in particular bulk silicon samples, usingphotoluminescence measurements.

In accordance with a first aspect of the present invention there isprovided a method of conducting an analysis of a semiconductor material,said method including the steps of: (a) exciting said material toproduce photoluminescence; (b) measuring the intensity of thephotoluminescence emitted from said material; (c) normalising themeasured photoluminescence intensity with regard to variations in thebackground doping density of said material to obtain a normalisedphotoluminescence intensity; and (d) analysing said normalisedphotoluminescence intensity in terms of one or more properties of saidmaterial.

Preferably a substantial area of the material is excited, and themeasuring step images the photoluminescence emitted from the area. Inpreferred embodiments the material is a silicon ingot or a siliconbrick, and the method is applied to at least one side facet of the ingotor brick. In one preferred form the background doping density ismeasured experimentally. Alternatively, the background doping density isdetermined empirically or calculated using a theoretical relationship.Preferably, the normalised photoluminescence intensity is interpreted asa measure of the effective minority carrier lifetime of the material.Alternatively, the normalised photoluminescence intensity is convertedto a measure of the bulk minority carrier lifetime of the material usinga predetermined theoretical relationship between bulk lifetime andnormalised photoluminescence intensity. In preferred embodiments thetheoretical relationship is applied to multiple samples of said materialwith similar surface preparation. In other preferred embodiments theproperty is the area or volume density of dislocations in the material.

In accordance with a second aspect of the present invention there isprovided a method of conducting an analysis of a silicon ingot or brick,said method including the steps of: (a) exciting at least a portion ofat least one side facet of said silicon ingot or brick to producephotoluminescence; (b) obtaining at least one image of thephotoluminescence emitted from said at least one portion of at least oneside facet; and (c) interpreting said at least one image in terms ofvariations in the area density of dislocations in said silicon ingot orbrick.

In one preferred form the photoluminescence images obtained fromdifferent side facets of the ingot or brick are analysed to obtain anestimated area density of dislocations within wafers subsequently cutfrom the ingot or brick. In another preferred form, at least onephotoluminescence image is used to highlight regions of the ingot orbrick of insufficient quality for wafer production.

In accordance with a third aspect of the present invention, there isprovided a method of conducting an analysis of a silicon ingot or brick,said method including the steps of: (a) exciting at least one side facetof said silicon ingot or brick to produce photoluminescence; (b)obtaining at least one image of the photoluminescence emitted from saidat least one side facet; and (c) interpreting said at least one image toidentify low effective and/or bulk minority carrier lifetime regionswithin said ingot or brick.

In accordance with a fourth aspect of the present invention, there isprovided a method of conducting an analysis of a semiconductor material,said method including the steps of (a) exciting a portion of saidmaterial to produce photoluminescence; (b) measuring the distribution ofthe photoluminescence emitted from said portion; (c) normalising themeasured photoluminescence distribution with regard to variations in theeffective minority carrier lifetime across said portion; and (d)analysing the normalised photoluminescence distribution in terms ofvariations in the background doping density of said material across saidportion.

Preferably, the material is a silicon ingot or a silicon brick, and themethod is applied to at least one side facet of the ingot or brick. Theportion is preferably in the form of a line scan or a two-dimensionalarea. The method is preferably applied to an ingot, brick or wafer ofupgraded metallurgical grade silicon. Preferably, the position of aminimum in the distribution of the photoluminescence is fitted to obtainthe ratio of donor and acceptor concentrations in the feedstock of theupgraded metallurgical grade silicon. In one preferred form the step ofnormalising with regard to variations in effective lifetime is omitted,and the photoluminescence distribution is interpreted in terms ofbackground doping variations. Preferably, the position of a minimum inthe photoluminescence distribution is used to identify the position of atransition region from p-type to n-type in upgraded metallurgical gradesilicon.

In accordance with a fifth aspect of the present invention there isprovided a method of conducting an analysis of a silicon ingot or brick,said method including the steps of: (a) obtaining at least twophotoluminescence measurements of at least one side facet of saidsilicon ingot or brick, said at least two photoluminescence measurementsbeing obtained with different detection wavelength bands; (b)calculating intensity ratios between at least two of saidphotoluminescence measurements; and (c) converting said intensity ratiosinto bulk lifetime or bulk diffusion length using a predeterminedtheoretical relationship. Preferably, the different detection wavelengthbands are provided by one or more dielectric filters, and the methodfurther comprises the step of normalising the photoluminescencemeasurements or the intensity ratios for angular variations in thetransmission of the one or more dielectric filters.

According to a sixth aspect of the present invention, there is provideda method of conducting an analysis of a silicon ingot or brick, saidmethod including the steps of: (a) obtaining at least twophotoluminescence measurements of at least one side facet of saidsilicon ingot or brick, the photoluminescence in said at least twophotoluminescence measurements being generated with different excitationwavelengths; (b) calculating intensity ratios between at least two ofsaid photoluminescence measurements; and (c) converting said intensityratios into bulk lifetime or bulk diffusion length using a predeterminedtheoretical relationship.

In any of the above aspects of the present invention, thephotoluminescence measurements or images are preferably used as acutting guide in wafer production or as a guide in wafer production tosort wafers into quality bins. Alternatively, the information obtainedfrom the method is used to improve the manufacturing of silicon bricksor ingots, or to determine the price of wafers derived from thematerial, or to obtain feedback on feedstock quality in the productionof silicon wafers.

According to a seventh aspect of the present invention, there isprovided a system for conducting an analysis of a semiconductormaterial, said system including: a photodetection unit for obtaining atleast one image or line scan of photoluminescence generated from asurface of said material; and a processor for normalising the measuredphotoluminescence intensity with regard to variations in the backgrounddoping density across said surface, and for analysing the normalisedphotoluminescence intensity in terms of one or more properties of saidmaterial.

According to an eighth aspect of the present invention, there isprovided a system for conducting an analysis of a silicon ingot orbrick, said system including: a photodetection unit for obtaining atleast one image or line scan of photoluminescence generated from atleast one side facet of said silicon ingot or brick; and a processor forinterpreting said at least one photoluminescence image or line scan interms of variations in the area density of dislocations in said siliconingot or brick.

According to a ninth aspect of the present invention, there is provideda system for conducting an analysis of a silicon ingot or brick, saidsystem including: a photodetection unit for obtaining at least one imageor line scan of photoluminescence generated from at least one side facetof said silicon ingot or brick; and a processor for interpreting said atleast one photoluminescence image or line scan to identify defect-richlow effective and/or bulk minority carrier lifetime regions within saidingot or brick.

According to a tenth aspect of the present invention, there is provideda system for conducting an analysis of a semiconductor material, saidsystem including: a photodetection unit for obtaining at least one imageor line scan of photoluminescence generated from a surface of saidmaterial; and a processor for normalising the measured photoluminescenceintensity in each part of said image or line scan with regard tovariations in the effective minority carrier lifetime across saidsurface, and for analysing the normalised photoluminescence image orline scan in terms of variations in the background doping density acrosssaid surface.

According to an eleventh aspect of the present invention, there isprovided a system for conducting an analysis of a silicon ingot orbrick, said system including: a photodetection unit for obtaining atleast two measurements of photoluminescence generated from at least oneside facet of said silicon ingot or brick, said at least twomeasurements being obtained with different detection wavelength bands;and a processor for calculating intensity ratios between at least two ofsaid measurements, and for converting said intensity ratios into bulklifetime or bulk diffusion length using a predetermined theoreticalrelationship. Preferably, the system further includes one or moredielectric filters for providing the different detection wavelengthbands, wherein the processor is further configured to normalise themeasurements or the intensity ratios for angular variations in thetransmission of the one or more dielectric filters.

According to a twelfth aspect of the present invention, there isprovided a system for conducting an analysis of a silicon ingot orbrick, said system including: first and second excitation units emittingfirst and second wavelengths for generating photoluminescence from atleast one side facet of said silicon ingot or brick; a photodetectionunit for obtaining first and second measurements of photoluminescencegenerated with said first and second excitation wavelengths; and aprocessor for calculating intensity ratios between said first and secondmeasurements, and for converting said intensity ratios into bulklifetime or bulk diffusion length using a predetermined theoreticalrelationship.

Preferably, the system according to any one of the seventh to twelfthaspects of the present invention further includes: an optical sourceemitting light with wavelength longer than the band-gap of silicon or ofsaid semiconductor material; and a detector for measuring thetransmission of said light through said silicon or semiconductormaterial.

In any one of the seventh to twelfth aspects of the present invention,the photodetection unit preferably includes a silicon camera.Alternatively, the photodetection unit includes an InGaAs camera.

According to a thirteenth aspect of the present invention, there isprovided a system when used to implement the method according to any oneof the first to sixth aspects of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Benefits and advantages of the present invention will become apparent tothose skilled in the art to which this invention relates from thesubsequent description of exemplary embodiments and the appended claims,taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates the sawing of silicon ingots into bricks and wafers;

FIG. 2 is a cross sectional side view of a silicon ingot illustratingthe typical variation of effective minority carrier lifetime;

FIG. 3 shows a PL image of the side facet of a conventional castmulticrystalline p-type silicon brick;

FIG. 4 shows a PL image of the side facet of a multicrystalline UMGsilicon brick;

FIGS. 5( a) and 5(b) show excess carrier density profiles calculated fora 15 cm thick silicon brick for two different excitation wavelengths(indicated by the different absorption coefficients) and for differentvalues of the bulk lifetime;

FIG. 6 shows theoretical relationships between normalised PL count rateand bulk minority carrier lifetime for a 15 cm thick silicon brick(circles) and a 200 μm thick silicon wafer (squares);

FIG. 7 shows plots of detected PL intensity versus bulk lifetime for a15 cm thick silicon brick, for PL measured in two different spectralregions, as well as the intensity ratio;

FIGS. 8( a) to 8(e) illustrate the conversion of a raw PL image of theside facet of a p-type silicon brick (FIG. 8( a)) to a bulk lifetimeimage (FIG. 8( e));

FIG. 9 shows a plot of intensity ratio versus bulk lifetime for PLgenerated from a 15 cm thick silicon brick by two different excitationwavelengths;

FIG. 10 shows a line scan of the PL intensity from bottom to top of thebrick shown in FIG. 4, as well as the calculated effective dopingdensity;

FIG. 11 illustrates how PL emission from an extended sample encountersan optical filter at a range of incidence angles;

FIGS. 12( a) to 12(d) and 13(a) to 13(d) illustrate the correction of aPL intensity ratio image for the dependence of dielectric filtertransmission on incidence angle; and

FIGS. 14( a) and 14(b) illustrate the conversion of an intensity ratioimage for PL measured in two different spectral regions (FIG. 14( a)) toa bulk lifetime image (FIG. 14( b)).

DETAILED DESCRIPTION

Preferred embodiments of the invention will now be described, by way ofexample only, with reference to the accompanying drawings.

The present invention relates mainly to PL imaging measurements on‘bulk’ silicon samples (e.g. bricks and ingots) prior to cutting intowafers. Specific advantages in relation to extracting bulk lifetimeinformation from PL images on bricks in comparison to wafers aredisclosed. The present invention details the following principal ideas,which will be described in more detail and in the same sequence below:

1.) Using information about the background doping and its spatialvariation to normalise the PL image and thereby obtain more accuratequantitative information on effective or bulk lifetime variations.Specific benefits of PL imaging on bricks/ingots compared to wafermeasurements for determination of bulk lifetime images, especially theability to obtain bulk information over a much wider range of bulklifetime values and at a well defined injection level, are disclosed.

2.) The relative variation of the PL intensity, even without normalisingfor variations of the background doping, is often sufficient to identifyspecific important sample features such as low lifetime regions and highdislocation density regions.

3.) Using combinations of PL images taken under different experimentalconditions, such as different illumination or detection wavelengths orboth, one can eliminate the influence of doping variations, allowingdirect correlation of intensity ratios with bulk material quantitiessuch as bulk minority carrier lifetime or bulk diffusion length. Whilethe use of different detection wavelengths (obtained with differentspectral filters in front of the camera lens) has been disclosed inpublished PCT patent application No WO 2008/014537 A1, entitled‘Determining diffusion length of minority carriers using luminescence’and incorporated herein by reference, some specific and previouslyundisclosed advantages apply when this approach is applied to PL imagestaken on silicon bricks or ingots.

4.) The fact that PL images display the product of effective lifetimeand background doping enables one to get information about relative orabsolute variations of the background doping within the sample afternormalising the measured PL signal for variations in the minoritycarrier lifetime. In specific cases an as-measured PL image revealsimportant information about doping variations without suchnormalisation.

5.) The dependence of bulk lifetime on injection level is simplifiedconsiderably for PL analysis of bulk silicon samples. PL images aretypically measured with spatially constant illumination intensity, sodifferent lifetime values within the same image taken on a silicon waferare reported at different injection levels. The situation issurprisingly different for lifetime measurements taken on bulk siliconsamples (such as bricks) under typical excitation conditions for PLimaging. Such measurements allow lifetime values within a considerablerange to be measured in a single image taken with spatially constantillumination and at a well defined constant average injection level.

The PL techniques of the present invention have particular applicationto the characterisation of silicon bricks and ingots prior to wafering.Specific applications include determination of dislocation densitieswithin a brick, acquisition of bulk lifetime images on the side facetsof a brick, localisation and quantification of low lifetime regionswithin an ingot caused by high impurity concentrations, and measurementof the doping transition region in compensated or UMG silicon bricks orwafers. As will be explained in more detail below, manufacturers ofbricks and wafers can for example use this information to improve themanufacturing conditions of ingots or as a cutting or sorting guide foringots, bricks or wafers. The PL techniques can also be combined withinfrared techniques (described above) to provide more completeinformation about structural and electronic properties of bricks. A newexperimental system could combine PL imaging and infrared transmissionin one tool that could be used either for off-line characterisation orsampling or for in-line characterisation of one or more surfaces ofbricks during manufacturing.

Examples of how PL measurements can be used to improve the manufacturingconditions of ingots or as a cutting/sorting guide for bricks or wafersinclude the imaging of dislocation distributions, low lifetime regions,bulk lifetimes and compensated regions of UMG bricks, allowing defectiveregions to be discarded or manufacturing conditions to be improved. Withreference to FIG. 2, fewer bricks may be produced if larger parts of thelow lifetime regions 10 of an ingot are discarded during cutting,yielding a smaller number of bricks but the bricks will be of betterquality.

FIG. 3 shows an example of a PL image on the side facet of aconventional cast p-type brick, revealing regions with high and lowdislocation densities (dark regions 12 and bright regions 14respectively), allowing estimation of the dislocation density withinwafers that will be cut from that brick. Using PL images taken on morethan one brick facet, a more reliable estimate of the dislocationdensity in subsequent wafers can be obtained. This analysis may beperformed in combination with application of suitable image processingalgorithms. One or several PL images on the side facets of a brick willprovide information about the position of dislocation rich areas and mayallow wafer manufacturers to sort wafers into quality bins (including areject bin) simply based on information from PL images taken on thebrick prior to wafering and on knowledge of the wafer position withinthe brick. The information may also provide a wafer manufacturer withrapid feedback on feedstock quality.

A PL image of a side facet of a UMG silicon brick is shown in FIG. 4.The dark band 16 visible near the top of the image (corresponding to aregion near the top of the brick) represents the p-type to n-typetransition region with effectively zero doping density. The PL image canthus be used to gain information quickly about the position of thetransition region, allowing that part of the brick to be removed (sinceit cannot be used to manufacture solar cells) and separation of p-typewafers from n-type wafers. In combination with modelling, the positionof the dark band in the PL image can also be used to calculate the ratioof doping atom concentrations in the feedstock, as described below.

Wafers that are cut from the bottom and top of a brick, and wafers thatcontain low lifetime regions around the edge as a result of impuritiesfrom the crucible walls, may produce lower efficiency solar cells. Asshown in FIG. 3, low lifetime regions 10 appear dark in a PL image, sothat one or several PL images on the side facets of a brick will provideinformation about the position of impurity-rich areas and may allowwafer manufacturers to sort wafers into quality bins (including a rejectbin) simply based on the information from the PL images taken on thebrick prior to wafering and on knowledge of the wafer position withinthe brick.

Wafer manufacturers can use bulk lifetime images on the side facets ofbricks for more efficient and more reliable process monitoring andcontrol than is possible with variations in uncalibrated or effectivelifetimes. Bulk lifetime measurements obtained with any of the methodsdisclosed here can be used as an R&D tool for process optimisation anddebugging. Bulk lifetime information obtained from measurements on thebrick may also be used to sort wafers into different quality bins basedon their position within the brick. Such binning may be based on theinformation obtained from one or more PL images taken on one or moreside facets of the ingot. The bulk lifetime information can also be usedfor fast feedback on feedstock quality.

The general concept of capturing PL images is described in theabovementioned published PCT patent application number WO 2007/041758A1. The basis of PL imaging is that a substantial area of a sample isilluminated with light suitable for exciting photoluminescence from thesample, and the photoluminescence emitted from the illuminated areaand/or from surrounding areas is imaged with a multi-pixel detector suchas a silicon CCD camera. As such it is to be distinguished from the muchslower PL mapping technique, described in U.S. Pat. No. 7,113,276 forexample, where photoluminescence is generated by a focussed laser beamscanned point-by-point across a sample surface. It should be noted thatthe illuminated and imaged areas need not coincide; as disclosed in PCTpatent application No PCT/AU2010/000577 entitled ‘Material or devicecharacterisation with non-homogeneous excitation’ and incorporatedherein by reference, it can be advantageous for example to illuminateone or more selected regions of a sample surface and image thephotoluminescence emitted from nearby non-illuminated regions as well asfrom the illuminated regions.

PL imaging can be useful if one wants to observe the two-dimensionaldistribution of features such as dislocations or high impurity areas.However for large specimens such as silicon bricks or ingots it may beimpractical if not impossible to obtain a single PL image of the area ofinterest, and it may therefore be necessary to stitch together two ormore individual images to form a composite image. Such stitching may benecessary for example if the available light sources have insufficientpower to illuminate the required area with sufficient intensity, or ifhigher spatial resolution than is possible with a single image isrequired. To acquire a composite image it is necessary to scan thesample and the illumination/detection system relative to each other.Possible scanning methods include: ‘step and image’, where a small areasection is imaged and either the sample or the imager is moved onto thenext section; ‘scan and image’, where the imager measures a fixed smallarea unit but is constantly in motion sweeping back and forth relativeto the sample; or ‘sweep imaging’, where for example a line imager thefull width of the sample is moved lengthwise relative to the sample. Thestitching may be implemented in an automatic fashion using suitableimage processing. When used in this specification, the terminology ‘PLimage’ thus includes both single PL images and composite imagesgenerated from two or more individual images.

In other situations it may be unnecessary to obtain a two-dimensional PLimage. For example if the quantity to be measured varies significantlyin only one direction, such as the doping density in a silicon brick oringot, a PL line scan will often be sufficient. A PL line scan can beacquired for example in a single frame with a line camera, or byscanning a point source across the sample surface in the requireddirection. There are also situations where a single PL measurement willsuffice, for example to obtain an average measure of a quantity over acertain area. In this specification the inventive principles areprimarily described with respect to PL area imaging, but it should beunderstood that they also apply to other forms of PL measurements,including line scans and single points.

1) Determination of Bulk Lifetime in Bricks and Ingots from PL Imaging

Bulk lifetime images of bricks and ingots are obtained from PL images inthe following sequence:

(i) Measure a PL image;

(ii) Convert the measured PL count rate (or intensity) in each pixelinto a normalised count rate (or intensity) PL_(norm) that is normalisedwith regard to spatial background doping density variations andoptionally also with regard to variations in measurement parameters suchas exposure time, pixel binning (i.e. the number of pixels binned in theX-direction multiplied by the number of pixels binned in theY-direction), incident light intensity and collection optics efficiency;

(iii) Convert the resulting normalised image into an absolute bulklifetime image using a predetermined theoretical or empiricalrelationship.

Step (i) has been described in the abovementioned published PCT patentapplication number WO 2007/041758 A1, and includes the possibility ofcreating a composite PL image by stitching together two or more imagestaken on different parts of the same sample surface.

Step (ii) can be performed with experimental data for the backgrounddoping density or, if the background doping density is sufficientlypredictable in production, based on theoretical or empirical data. Insingly doped silicon (i.e. p-type or n-type silicon that contains onedominant type of doping atom), the background doping density can beobtained from resistivity measurements using tabulated data for themobilities of electrons and holes for the conversion of resistivity intodoping density. The resistivity can be measured by several methodsincluding contact measurements (four point probe) and non-contactmeasurements (e.g. inductive coil, Eddy current, surface voltage). Thesetechniques (among others) can provide spatially resolved informationabout the doping density when performed in a scanning mode or by usingmore than one sensor located in different positions, or by a combinationthereof. To reduce the measurement time, a two dimensional distributionof the doping density may be measured with coarse spatial resolution,which is then used to normalise the PL image after suitableinterpolation or extrapolation of the data. Coarse spatial informationabout the background doping density is sufficient in many practicalcases since long range resistivity variations are more typical thansmall scale/short range variations.

Alternatively, in the case of side facets of ingots or bricks, one ormore line-scans of the doping density from top to bottom may besufficient, since the strongest relative variations occur predominantlyin only one direction, e.g. from bottom to the top of an ingot or brick.

In another alternative the measured doping density variation may befitted with an expected theoretical relationship (e.g. the Scheilequation) and the doping variation across the entire sample area thencalculated for each pixel from that equation. The experimental data thatform the basis of the fitting can be a two-dimensional map or one ormore line scans or even just one or more single measurement pointsacross the surface. The influence on the analysis of noise in the dopingdensity data, unavoidable in experimental data, is thereby avoided. Inaddition, some measurement techniques such as the Eddy current techniquegenerate artefacts in the measured resistivity near the edges ofsamples. In such cases the experimental data would require correction ofthese artefacts or extrapolation of the data from regions unaffected bythe artefacts. Some fitting and extrapolation routines are thereforerequired in any case.

In yet another alternative, no measurement of the doping is performed atall, and the variation of the doping density is determined solely from atheoretical relationship or from statistical/empirical production data.

Whatever experimental or theoretical method is used to determine thedoping density, that information, along with the measurement time, pixelbinning settings and variations (experimentally measured or modelled) inthe incident illumination intensity and collection optics efficiency ifrequired for improved accuracy, is used to convert the measured PL datainto PL_(norm). The resulting normalised PL data is indicative ofrelative variations in effective minority carrier lifetime across theimage area.

Step (iii), the conversion of the normalised PL intensity PL_(norm) intobulk lifetime τ_(bulk) can be performed based on an empiricallydetermined relationship PL_(norm)=f_(empirical)(τ_(bulk)) that can beobtained by calibrating experimental normalised PL data from one or moresamples against bulk lifetime data obtained on those same samples bysome other means. Techniques (such as QSSPC) for measuring the effectivelifetime, with known relation between bulk and effective lifetimes, maybe applied to obtain the bulk lifetime data. These other measurementtechniques may be performed on a calibration sample after surfacepassivation for more reliable results. Alternatively, a calibrated PLimage taken on a passivated sample may be used as the reference bulklifetime data for the determination of the empirical relationship. Asdiscussed above the injection level has an important impact on the bulklifetime, so that calibration of PL data versus any other techniqueneeds to be performed with both measurements at the same or similarinjection level.

Apart from the bulk lifetime and the doping density, the main variablesaffecting the detected PL intensity from an unpassivated silicon brickare the surface properties of the sample, specifically the surfacetexture, reflectance and depth and severity of sawing-induced surfacedamage. In practice the same empirical relationshipPL_(norm)=f_(empirical)(τ_(bulk)) may be used for bricks/ingots at thesame stage in a production line, since the surface properties can beexpected to be sufficiently similar. However separate empiricalrelationships may have to be determined for ingots/bricks at differentproduction stages (e.g. polished bricks versus as-cut unpolishedbricks). In production the calibration correlationPL_(norm)=f_(empirical)(τ_(bulk)) for samples at a specific processingstage may have to be checked and updated on a regular basis.

Conversion of the normalised PL intensity into bulk lifetime can also beperformed based on a predetermined theoretical relationshipPL_(norm)=f_(theoretical)(τ_(bulk)). Calculation of this relationship isbased on analytically or numerically calculating the depth-dependentminority carrier density Δn(y) within the sample for given illuminationconditions, where y is the distance from the surface. FIGS. 5( a) and5(b) show carrier profiles in a 15 cm thick silicon brick for twodifferent absorption coefficients of the excitation light (implyingdifferent excitation wavelengths). In each graph the depth dependentcarrier density is shown for three values of the bulk minority carrierlifetime: τ_(bulk)=10 μs (plot 18); τ_(bulk)=100 μs (plot 20); andτ_(bulk)=1000 μs (plot 22). Such calculations can be performed usinganalytical models for the excess carrier density or numerical modellingpackages such as DESSIS or PC1D. The detected PL rate can then becalculated by integrating the rate of spontaneous emission over thethickness of the sample and over the emission spectrum, taking intoaccount re-absorption within the sample, the sensitivity of the detectorand the transmission of filters, as described for example in T. Trupke,‘Influence of photon reabsorption on quasi-steady-statephotoluminescence measurements on crystalline silicon’, Journal ofApplied Physics 100, 063531 (2006). Performing these calculations for arange of different bulk lifetime values allows one to calculate thetheoretical relationship PL_(norm)=f_(theoretical)(τ_(bulk)).

Calculations as described above can in principle provide a quantitativerelationship between the normalised PL count rate (indicative of theeffective lifetime) and the bulk lifetime. In practice however, thesecalculations generally provide only a relative relationshipPL_(norm)=C*f_(theoretical)(τ_(bulk)), because of uncertainties inassumptions that have to be made about various hardware parameters andsample properties. The scaling factor C will be constant or very similarfor different samples (bricks) at the same processing stage, but mayhave to be determined separately for bricks at different processingstages. In principle therefore, for measurements on bricks in productionat the same processing stage (e.g. after polishing), calibration of ameasurement system only needs to be performed once for a specifichardware system, although in practice the calibration could be repeatedat regular intervals to monitor and compensate for drifts of hardwarecomponents for example. The determination of C is performed in a similarway as described above, by comparison with actual bulk lifetime datadetermined from some other technique. Alternatively C may be determinedby comparison with another calibrated PL imaging system. A single datapoint is sufficient for that calibration, but for more reliable resultsthe average of two or more data points from one or more samples may beused. For example the calibration constant may be determined bycomparison of cross sections or histograms of bulk lifetime taken on oneor more facets of silicon bricks.

The self-consistent measurement techniques described below thatdetermine bulk lifetime from combinations of images taken underdifferent conditions may also be used to calibrate the system.

FIG. 6 shows example theoretical relationships between normalised PLcount rate (indicative of effective lifetime) and bulk lifetime thatwere calculated as described above, for an unpassivated 15 cm thicksilicon brick (circles) and for an unpassivated 200 μm thick siliconwafer (squares). These relationships are highly non-linear, andinspection of the two curves highlights an unexpected benefit of PLmeasurements on bulk samples such as bricks or ingots, compared tothinner samples such as unpassivated wafers. For the unpassivated waferthe normalised PL count rate saturates for bulk lifetime values largerthan τ_(bulk)˜10 μs, whereas for the brick it continues to varysignificantly at much higher bulk lifetime values, with no saturationfor bulk lifetime values of up to ten milliseconds. The saturationobserved in the wafer is caused by the diffusion length becoming largerthan the thickness for bulk lifetimes greater than ˜10 μs, in which casefurther increasing the bulk lifetime or bulk diffusion length does notincrease the total carrier density in the sample. A common descriptionof this phenomenon is that the effective carrier lifetime becomeslimited by the surfaces. In contrast, for the much thicker brick samplethe diffusion length remains small compared to the thickness, so thatthe carrier density within the brick keeps increasing with the diffusionlength and does not become surface limited. An important consequence ofthis is that in principle PL signals obtained from unpassivated brickscan be reliably converted into bulk lifetime or bulk diffusion lengthdata over a much wider range of bulk lifetime values than is possiblefor unpassivated wafers.

Calculations of normalised PL intensity as a function of bulk lifetime(such as those shown in FIG. 6) show that the actual shape of the curvedepends on the spectral sensitivity of the apparatus used to measure thePL, which is generally determined by the spectral sensitivity of thecamera and the transmission of filters in front of the camera. Enhancingthe spectral sensitivity at longer wavelengths causes a stronger(steeper) dependence of the normalised PL signal on bulk lifetime,allowing a more accurate conversion of PL intensity into bulk lifetime.This effect is visible in the graphs shown in FIG. 7, which compare theexpected variation in PL signal from a selected region of a 15 cm thicksilicon sample as a function of bulk lifetime for two differentdetection wavelength intervals, 950-1000 nm (squares) and >1050 nm(circles). The higher sensitivity of the PL signal at longer wavelengthsarises because longer wavelengths probe the carrier density deeperinside the sample (e.g. a brick), where most of the variation of theexcess carrier density occurs for long bulk lifetimes (compare FIG. 5(b)). In practice this long wavelength sensitivity enhancement may beachieved either by enhancing the relative long wavelength sensitivity byintroducing into the detection system long pass filters with cut-onwavelength in the 1000-1200 nm range, or by enhancing the absolute longwavelength sensitivity by using a detector that is more sensitive atlonger wavelengths, for example an InGaAs camera instead of a siliconcamera.

An example of the conversion of a raw PL image to a bulk lifetime imagewill now be explained, with reference to FIGS. 8( a) to 8(e). FIG. 8( a)shows a PL image 24 acquired from the side facet of a p-type siliconbrick, and FIG. 8( b) shows a representative distribution 26 of thep-type dopant (boron) across the side facet, the greyscale representingthe dopant concentration. The dopant distribution was calculated fromthe Scheil equation, with the maximum dopant concentration 28 at the topof the brick. Bearing in mind that the intensity variation in a PL imageis determined by the product of the doping concentration and theeffective minority carrier lifetime, the PL image of FIG. 8( a) isnormalised by the dopant distribution of FIG. 8( b) to yield thenormalised PL image 30 shown in FIG. 8( c). Intensity variations in FIG.8( c) are indicative of variations in effective minority carrierlifetime. To convert effective lifetime to bulk lifetime, the normalisedPL image 30 is corrected using the representative non-linearrelationship between effective lifetime and bulk lifetime shown in FIG.8( d) to produce the bulk lifetime image 32 of FIG. 8( e), showingvariation of bulk lifetime across the side facet of the sample brick.Note that in this illustrative example, the particular non-linearrelationship in FIG. 8( d) is a simple cubic equation, used to representan actual empirical or theoretical relationship of the type shown by thefilled circles in FIG. 6.

2) Interpretation of Relative Intensity Variations in PL Images onBricks/Ingots

Step ii) in the above example application, i.e. the normalisation of PLcount rate with regard to background doping density and optionallyvariations in measurement parameters, may not be required for somespecific applications, where absolute count rates are of secondaryconcern and where PL images are analysed in terms of specific patternsor relative variations. Two examples are the identification of regionswith high dislocation density (as shown in FIG. 3 for example) and theidentification of low lifetime regions at the top, the bottom and theside walls of a brick or ingot (as shown in FIGS. 2 and 3 for example).Image processing algorithms may be applied to distinguish such featureswithin the images from other features in the image.

The dislocation density observed in PL images of side facets of bricksmay be used to estimate the dislocation density in wafers cut from thatbrick, and to estimate the volume density of dislocations within thebrick as a function of height within the brick. That information may beused for quality binning and sorting of wafers. These estimates willbecome more accurate by combining the information from PL images takenon more than one, up to four side facets of the brick.

Similarly, a PL image on a side facet of a brick can be used to identifythe position and expanse of low lifetime regions at the top, bottom, andin some cases the side walls. Again, such analyses will be more accurateif PL images of more than one, up to all four side facets are combined.PL images taken on the brick may be also used to predict the lifetimedistribution in wafers cut from that brick; for example the low lifetimeregion 10 (dark area) on the right hand side of the image shown in FIG.3 will result in a low lifetime region near the edge of wafers slicedfrom that portion of the brick. PL images of the side facets of ingotsmay also be used to guide the cutting of the ingots into bricks.

3) Combining Images Taken Under Different Measurement Conditions (a)Different Detection Wavelengths

In the abovementioned published PCT patent application number WO2008/014537 A1 we described a technique whereby at least twoluminescence images are taken with different spectral filters mounted infront of the camera lens. Since long wavelength luminescence has ahigher average optical path length within the sample beforere-absorption, measurements with different filters in front of thedetection system allow capture of luminescence emitted from differentdepths in the sample. It was shown that the ratio of luminescenceintensities measured with two different filters can be converted intobulk diffusion length. Compared to electroluminescence (EL) images onfinished solar cells, it has been shown that this approach has theadvantage that local variations of the diode voltage, normally presentduring EL imaging on cells, cancel out in the luminescence intensityratio so that the intensity ratio of two uncalibrated images providesthe diffusion length in absolute units.

The basis for this method is that the relative carrier density profileacross the thickness of a sample changes with the diffusion length, butthis method becomes insensitive to variations in diffusion length oncethe diffusion length is a few times larger than the sample thickness.The same argument applies in the context of applying a similar techniqueto bricks that are typically >10 cm thick, however now the condition ofthe diffusion length being smaller than the sample thickness isfulfilled over a much wider range of values, more specifically for allpractical values of interest for silicon. Variations of the bulklifetime or the bulk diffusion length thus have an influence onluminescence intensity ratios over a much wider range of bulk lifetimeor bulk diffusion length values in bricks than is the case for wafers orcells.

Applying the above method of calculating intensity ratios of imagestaken with identical excitation but variable detection conditions hastwo benefits: firstly, variations of the background doping across abrick are eliminated from a PL intensity ratio; and secondly the ratioof two uncalibrated PL images, each in relative units (each measuredwith the same incident light intensity and each normalised for thecamera exposure time and binning) provides the absolute bulk lifetime orbulk diffusion length without a need for external calibration.

This method may be applied as follows:

Step (i): measure two PL images with the same or similar illuminationintensity but with two different wavelength detection bands. Preferablyone measurement should be of short wavelength photons, to yield enhancedinformation about the carrier density near the front surface, whereasthe second measures longer wavelength photons, thereby measuring theaverage carrier density up to a specific depth of the sample.

Step (ii): optionally normalise each image with regard to the cameraexposure time and binning, and if necessary with regard toexperimentally measured or modelled variations in the illuminationintensity and/or the efficiency of the collection optics.

Step (iii): for each pixel calculate the intensity ratio from the twonormalised images.

Step (iv): for each pixel convert the calculated intensity ratio intobulk lifetime using a predetermined relationship.

Alternatively, a combined normalisation for variations in theillumination intensity and/or the efficiency of the collection opticscan be applied to the intensity ratio, rather than to the individualimages. The predetermined relationship from step (iv) can be determinedempirically by comparison of experimental PL intensity ratios withexperimental bulk lifetime or bulk diffusion length data, or obtainedtheoretically by calculating relative carrier profiles for a range ofdifferent bulk lifetime/diffusion length values analytically ornumerically with a common modelling program (e.g. DESSIS, PC1D), thenusing the carrier profiles to calculate the two expected measured PLintensities for each bulk lifetime/diffusion length value, taking intoaccount re-absorption and the spectral sensitivity of the sensor. Thesecalculations are performed separately for the two PL images. Theexpected PL intensity ratio is calculated for each bulklifetime/diffusion length, and an analytical curve or lookup table isgenerated for the intensity ratio as a function of bulklifetime/diffusion length.

FIG. 7 shows calculated data for the detected PL intensity as a functionof bulk lifetime in a 15 cm thick silicon sample. Referring to the lefthand Y-axis, the theoretical PL intensity acquired with a 950-1000 nmspectral range is plotted as filled squares, while the theoretical PLintensity acquired with >1050 nm is plotted as filled circles. Referringto the right hand Y-axis, FIG. 7 also shows the ratio of the two PLsignals as a function of bulk lifetime (open triangles), and it can beseen that the variation in the intensity ratio allows direct correlationwith the bulk lifetime. The fact that the two filter combinations yieldthe same PL count rate at low bulk lifetime values, resulting in unityintensity ratio, is a coincidence resulting from this specific choice ofwavelength intervals and the specific experimental conditions modelled.

If an InGaAs camera, an IR sensitised photoelectron multiplicationsilicon camera or similar sensor with significant spectral sensitivityin the 1100-1300 nm range were used with appropriate longer wavelengthfilters, one could detect variations of the carrier density deeperinside the brick, thereby enabling the detection of diffusion lengthvariations in a regime of still higher diffusion lengths.

The intensity ratio curve in FIG. 7 shows that the variations in theintensity ratio are strongest at high bulk lifetime values, so that themethod may be particularly useful for measurements on the side facets ofmonocrystalline ingots or bricks or the surfaces of high lifetimemulticrystalline bricks.

Dielectric filters are in principle well suited to the selection ofdifferent PL wavelength bands, because of their sharp cut-on or cut-offwavelength i.e. the transition from high to low transmission. Howeverthe transmission of dielectric filters has a strong angular dependence,whereby the cut-on/cut-off wavelength moves to shorter wavelengths withincreasing angle of incidence. This effect needs to be considered in thepresent application where, as shown in FIG. 11, PL emission 40 from anextended sample 42 such as a silicon wafer or brick impinges on adielectric filter 44 placed in front of the imaging camera 46 at a rangeof incidence angles. Clearly this will affect the PL intensitydistribution within individual PL images, and therefore the intensityratio and the analysis result. The effect will be even more pronouncedif a dielectric long pass (LP) filter is used to obtain the longerwavelength PL image and a dielectric short pass (SP) filter is used toobtain the shorter wavelength PL image, because the angular dependenceof the cut-on/cut-off wavelength has opposite effects on images acquiredthrough LP and SP filters. To explain, the shift in the cut-on/cut-offwavelength to shorter wavelengths with increasing angle of incidencemeans that a PL image acquired through an SP filter will have relativelyreduced intensity in the off-axis portions, while a PL image acquiredthrough an LP filter will have relatively increased intensity in theoff-axis portions.

There are a number of means for mitigating this problem that may beapplied individually or in combination. Inspection of FIG. 11 shows thatincreasing the distance between the camera 46 (and the filter 44) andthe sample 42 will reduce the range of incidence angles, within theconstraints of system design and the inevitable reduction in receivedsignal strength because of the approximately Lambertian pattern of PLemission from the sample surface.

Another method is to apply suitable corrections to the long and shortwavelength images, using flat field corrections measured for each filterto take into account the angular dependence of their transmission. Aflat field correction for a given filter may for example be obtained byacquiring through the filter a PL image of a high qualitymonocrystalline silicon wafer that can be expected to have uniform PLresponse across its area. The flat field correction thus derived willalso correct for other non-uniformities in the system, in particular theangular dependence of the efficiency of the collection optics. Becausedielectric filters may not be homogeneous across their area, it may alsobe necessary to measure the flat field correction for a specific filterorientation, and to maintain that orientation during subsequentacquisition of images. When calculating an intensity ratio of two imageswith different filters, one can either correct each image beforecalculating the ratio, or correct the intensity ratio image using acombined flat field correction.

To illustrate this correction procedure, FIGS. 12( a) and 12(b) show PLimages of a silicon solar cell acquired with a silicon CCD array througha 1000 nm SP filter and a 1050 nm LP filter respectively. FIG. 13( a)shows a profile of the PL intensity along a diagonal cross section ofthe FIG. 12( a) image, while FIG. 13( b) shows the corresponding profilefor the FIG. 12( b) image. The intensity profiles show high intensityregions 48 and low intensity regions 50 superimposed on a comb-likepattern 52 caused by the metal fingers, and low intensity spikes 54caused by the bus bars. It will be seen that the intensity of the FIG.12( a) (SP) image is significantly reduced in the corners, which ispartly due to the filter angular dependence described above. We notethat the intensity of the FIG. 12( b) (LP) image is also reduced in thecorners, although to a lesser extent than for the SP image; this isbecause the effect of the filter angular dependence, which tends toincrease the intensity in the corners, is outweighed by other effectssuch as the angular dependence of the collection optics. The image shownin FIG. 12( c) is an intensity ratio of the images shown in FIGS. 12( a)and 12(b), and FIG. 13( c) shows the PL intensity profile along adiagonal cross section, again showing a roll-off in the corners.Finally, FIGS. 12( d) and 13(d) show the flat field corrected intensityratio image and its corresponding PL intensity profile, and it is clearthat the angular dependence artefact has been removed.

Alternatively, absorption filters could be used to select the differentwavelength PL bands. Unlike dielectric filters their transmission haslittle dependence on the angle of incidence, however their absorptionedges are less steep resulting in inferior band selection/rejection.

We note that the FIG. 12( b) image, of longer wavelength PL emission, ismore blurred than the FIG. 12( a) image. This is because of the lowerabsorption of longer wavelength light in silicon, leading to lateralsmearing within the pixels of the silicon CCD camera. As discussed inpublished PCT patent application No WO 09/121,133, image contrast inthis circumstance can be enhanced by applying a theoretical orexperimentally measured point spread function for the optical detectionsystem.

An actual implementation of the intensity ratio method is illustrated inFIGS. 14( a) and 14(b). One side of a p-type multicrystalline siliconbrick was illuminated with ˜1 Sun of near IR light from a diode laserarray and the PL emission imaged by a Si CCD camera firstly through a1050 nm LP filter and secondly through a 1000 nm SP filter. Theintensity ratio of the images was calculated pixel by pixel, and theresulting ratio image is shown in FIG. 14( a), where the ratio rangesfrom 1 in low lifetime regions to 3 in high lifetime regions. For eachpixel, the intensity ratio was then converted into bulk lifetime using atheoretical relationship, with the resulting bulk lifetime image shownin FIG. 14( b). We note that because of the size of the brick it wasnecessary to acquire two images with each filter and stitch themtogether; the joins in FIGS. 14( a) and 14(b) are indicated by arrows.

It will be appreciated that using an optical filter to select thewavelength range of the PL decreases the intensity of the PL signal atthe camera, potentially increasing the image acquisition time andslowing the method down. In a variant embodiment, the short wavelengthand long wavelength PL images are acquired with reduced spatialresolution, but without compromising the signal to noise ratio, usingpixel binning, and the two images processed as described previously toobtain a reduced spatial resolution image of the bulk lifetime. A higherresolution PL image, i.e. without pixel binning, is then acquiredwithout optical filtering, and the data correlated to obtain a higherresolution image of the bulk lifetime. This embodiment requires theacquisition of a third PL image, but may be faster because the filteredimages can be acquired more rapidly. Comparison of the bulk lifetimedata obtained from the intensity ratio image with an unfiltered PL imagecan also be used to obtain information on the background dopingvariation within the sample.

(b) Different Excitation Wavelengths

In a similar fashion, absolute lifetime/diffusion length distributionscan be obtained from the ratio of PL images taken on bricks or ingotswith identical detection wavelength bands but with different excitationwavelengths that create excess carriers at different depths within thesample. FIG. 9 shows the luminescence intensity ratio between two PLimages obtained from a 15 cm thick silicon brick with 800 nm excitationand 600 nm excitation, as a function of the bulk lifetime.

The intensity ratio curve shown in FIG. 9 shows that this approachprovides absolute lifetime or diffusion length information only forshort diffusion lengths/lifetimes since the ratio of PL intensitiestaken with different excitation wavelengths is largely insensitive tobulk lifetime variations for values larger than 10 μs. For longerdiffusion lengths the excitation wavelength has no significant impact onthe relative carrier density profile so that the PL intensity ratiobecomes constant. However some of the same benefits as for measurementswith variation of the detection wavelength range still apply, in thatvariations of the background doping across a sample are eliminated froma PL intensity ratio, and the ratio of two uncalibrated PL images, eachin relative units (each measured with the same incident light intensityand normalised for the camera exposure time and binning) provides theabsolute bulk lifetime or bulk diffusion length without a need forexternal calibration.

(c) Different Detection and Excitation Wavelengths

It is also possible to determine the bulk properties of a sample bytaking the intensity ratio of two PL images in which both the excitationand detection wavelengths are varied between the two images.Alternatively the two approaches may be combined so that the intensityratio of two images taken with different detection wavelengths isanalysed in regions with high bulk lifetime, while the ratio of imagestaken with different excitation wavelengths is analysed in regions withlow bulk lifetime.

4) Obtaining Information about Variations in the Background Doping

The following applications are particularly useful for bricks and ingotsbut could in principle also be applied to wafers with lateral variationsof the doping density. Since the measured PL signal is proportional toboth the effective lifetime and the background doping density,information about the background doping density can be obtained bynormalising the measured PL intensity with regard to lifetime variationsmeasured in a separate lifetime measurement. Specifically, the methodsdescribed in section 3) above allow one to obtain the bulk lifetimewithout the need for calibration.

From any bulk lifetime variation data the expected normalised PLintensity variation can then be calculated from the relationship betweennormalised PL count rate and bulk lifetime as shown in FIG. 6. The ratiobetween a measured PL image and the PL intensities expected according tothe bulk lifetime will then give the relative doping density variationacross the sample. Specifically, this approach may be applied using bulklifetime data obtained from the methods described in section 3) above.In this case the PL image can be one of the two individual PL imagestaken with either different detection wavelength ranges or differentillumination wavelengths, or a third PL image. Alternatively, in caseswhere a separate measurement of the effective lifetime is performed, aPL image that is normalised with regard to effective lifetime variationsthen represents an image of the relative doping density variation.Either way, the relative doping density variation across the sample canbe calibrated into an absolute doping density image if either the dopingdensity at one point or the average doping density of the sample isknown. When applied to samples with similar surface properties inproduction the above calibration into absolute doping density may not benecessary on every sample. Instead, the same calibration constant may beapplied to different samples with similar or substantially identicaloptical surface properties (such as polished bricks).

In cases where the effective lifetime can be assumed to be constant, theas-measured PL intensity variation represents an image of the relativedoping density variation, which again can be calibrated into an absolutedoping density image if the doping density in one point or the averagedoping density of the sample is known. An example of a sample type wherethis assumption holds is unpassivated wafers with high bulk lifetime; inthese samples the effective lifetime (compare squares in FIG. 6) isconstant and the PL intensity directly reveals doping variations. Thiscan be used for example to measure doping striations in monocrystallinewafers.

In other specific cases the doping density variations are so dramaticthat small variations in the effective lifetime only cause a small errorthat may be insignificant for some applications. One such special caseconcerns compensated or UMG bricks, where in the transition region fromp-type to n-type the changes in the effective doping density are verypronounced, revealed in a deep minimum in the PL count rate. For examplein the PL image of a UMG brick shown in FIG. 4 the dark band 16 near thetop shows the exact position of the transition region, without the needto compensate the PL signal for lifetime variations. The ability tolocate the transition region quickly and accurately provides wafermanufacturers with a cutting guide to identify and sort wafers from thep-type, transition and n-type regions. The analysis discussed below isalso performed without taking into account variations in the lifetime;it is thus assumed that effective lifetime variations are much smallerthan the variations in effective doping density.

To illustrate the direct conversion of PL data to doping densityvariations, FIG. 10 shows (with reference to the left hand Y-axis) aline scan 34 from bottom to top (left to right) of the PL intensity inthe PL image shown in FIG. 4, and (with reference to the right handY-axis) the fitted theoretical effective doping density, i.e. theabsolute value of the difference between the boron and phosphorousconcentrations (dotted line 36), each calculated separately according tothe Scheil equation. In the absence of variations in effective lifetime,the PL intensity is expected to be proportional to that effective dopingdensity.

In calculating the theoretical effective doping density, the segregationcoefficients k_(eff) for boron and phosphorous in crystalline siliconwere taken from the literature. The only remaining fitting parameterswere the initial concentrations of boron and phosphorus in thefeedstock, N_(B)(0) and N_(P)(0); these parameters were varied toachieve the best fit between the effective doping in relative units 36and the as-measured PL intensity line scan 34. Variation of N_(B)(0) andN_(P)(0) results in variations in the absolute effective doping and ashift on the X-axis of the minimum in effective doping, and theseparameters were varied until the minimum coincided with the minimum ofthe PL intensity 38.

Fitting of the relative effective doping density to the PL intensitycross section, as shown in FIG. 10, thus allows quantification of theratio N_(B)(0)/N_(P)(0). This approach is based on the assumption thatthe feedstock contains only one major donor species and one majoracceptor species, and that both donor and acceptor atoms are distributedin accordance with the Scheil equation. Under these assumptions theapproach would work in a similar fashion for other doping atoms insilicon, such as gallium.

5) Influence of Injection Level on Minority Carrier Lifetime

It will be recalled from the Background section that under quasi steadystate conditions the effective minority carrier lifetime is inverselyproportional to the generation rate G and proportional to the minoritycarrier density, so that τ_(eff)=Δn/G. However the fact that minoritycarrier lifetime is also a function of injection level complicates knownlifetime measurement techniques. As discussed in S. Bowden and R. A.Sinton ‘Determining lifetime in silicon blocks and wafers with accurateexpressions for carrier density’, Journal of Applied Physics 102, 124501(2007) for the QSSPC technique for example, lifetime data can bereported either for constant illumination intensity (i.e. constant G),resulting in a different injection level for each effective lifetime (asis the case e.g. in PL images on wafers), or for constant injectionlevel, equivalent to reporting each lifetime for a differentillumination intensity. Both approaches have shortcomings in that theyreport data within specific lifetime ranges either at an injection levelor at an illumination intensity (or both) that may have little or norelevance to the operation of a solar cell.

In contrast, we have surprisingly found that a single PL image on a bulksilicon sample (such as a brick) allows measurement of the bulk lifetimeat a constant illumination level and at a constant well-defined averageinjection level over a wide range of bulk lifetimes. To understand thiscounter-intuitive result we need to consider the definition of averagecarrier density and generation rate. In lifetime measurements on wafers,Δn and G are commonly calculated as mean values averaged over the samplethickness. However as was pointed out in the above-mentioned Bowden andSinton paper, this approach is not meaningful for bulk samples such asbricks, because relative to the total sample thickness, significantexcess carriers are present only in a small volume near the illuminatedsurface (compare for example the carrier density profiles shown in FIGS.5( a) and 5(b)). Bowden and Sinton described an analytical methodologythat overcomes this problem by defining a weighted average carrierdensity Δn_(avg) and an effective sample width W_(eff). We adopt thosedefinitions here and use the notation of average excess carrier densityaccordingly.

Using the analytical model described in the abovementioned Bowden andSinton paper, excess carrier density was calculated as a function ofposition inside an unpassivated silicon brick for two values of theabsorption coefficient (α=700 cm⁻¹, corresponding to ˜800 nm incidentlight, and α=3.5 cm⁻¹, corresponding to ˜1100 nm incident light) andplotted in FIGS. 5( a) and 5(b) respectively. Note that the excesscarrier density is zero at the surface (position=0) because the surfaceis unpassivated. FIGS. 5( a) and 5(b) both show excess carrier densityversus position for three values of bulk lifetime: 10 μs (plot 18), 100μs (plot 20), and 1000 μs (plot 22). In each graph the intersections ofthe rectangles 40 (shown only for the τ_(bulk)=100 μs and τ_(bulk)=1000μs plots) with the axes indicate the values of Δn_(avg) and W_(eff).Comparison of the rectangles shown for short wavelength excitation(α=700 cm⁻¹) in FIG. 5( a) shows that the main variation in the carrierprofile with increasing bulk lifetime is in the effective width, whilethe average carrier density is almost constant. The same comparison forlong wavelength excitation (α=3.5 cm⁻¹) shows that the average carrierdensity (related to the average injection level) scales strongly withlifetime.

These observations are consistent with the following equation derived byBowden and Sinton:

$\begin{matrix}{{\Delta \; n_{avg}} = \frac{\alpha \; N_{s}L^{2}}{2{D\left( {{\alpha \; L} + 1} \right)}^{2}}} & (1)\end{matrix}$

where L is the diffusion length, D the diffusion coefficient, N_(s) thephoton flux entering the sample, and α the absorption coefficient. ForαL>>1, i.e. for short wavelength excitation (or long lifetimes) eqn (1)simplifies to

$\begin{matrix}{{\Delta \; n_{avg}} = \frac{\; N_{s}}{{2D\; \alpha}\;}} & (2)\end{matrix}$

implying that the average injection level becomes independent of thelifetime. On the other hand for αL<<1, i.e. for long wavelengthexcitation, and using the relation τ=L²/D, eqn (1) simplifies to

$\begin{matrix}{{\Delta \; n_{avg}} = \frac{\; {\alpha \; N_{s}\tau}}{2\;}} & (3)\end{matrix}$

implying that the average injection level is proportional to thelifetime τ.

Turning now to consideration of the influence of injection level on PLdata, we note that PL images are typically acquired with infraredexcitation around λ=800 nm. With the absorption coefficient α˜700 cm⁻¹in this range, the condition αL>>1 is fulfilled for L≧100 μm, adiffusion length equivalent to τ_(bulk)=3.5 μs in p-type silicon.Importantly, in the most relevant range τ_(bulk)>3.5 μs, a single PLimage taken with laterally constant illumination and with λ=800 nmexcitation thus yields variable lifetime at an almost constant averageinjection level. With D=27 cm² s⁻¹ and N_(s)=3*10¹⁷ cm⁻² s⁻¹(approximately equivalent to 1 Sun illumination), eqn (2) yieldsΔn_(avg)=8*10¹² cm⁻³, independent of lifetime.

The choice of near infrared wavelengths around λ=800 nm for excitationthus has the added benefit that for typical bulk lifetimes it results inan average injection level in the brick that is very close to theinjection level that would be present in a typical finished industrialsilicon solar cell at the maximum power point. Variation of theexcitation wavelength or of the illumination intensity (or both) allowsfine tuning of that injection level as required. Measuring lifetime datain this injection level range also facilitates the analysis and avoidsinaccuracies associated with injection level dependencies of materialparameters such as the carrier mobilities or the radiative recombinationcoefficient, which vary significantly only at higher injection levels.Within the fundamental limitations of an analytical model that defines aspatially averaged injection level within a brick, PL imaging thusprovides ideal conditions for bulk lifetime evaluation.

The small dependence of the average injection level on bulk lifetime inPL measurements taken with short wavelength excitation on bricks hasanother interesting implication, in that the injection level is thenalmost linearly dependent on the illumination intensity. Taking severalluminescence images of the same brick area but with differentillumination intensities allows measurement of the injection leveldependent lifetime for each point or for specific areas in the image.This can be achieved by normalising the measured images with regard tothe illumination intensity, followed by conversion of theintensity-normalised PL count into bulk lifetime, the latter conversionperformed as described previously.

Since the average injection level is proportional to the generation rateG, which is itself proportional to the incident light intensity, ameasured incident light intensity can be converted into an averageinjection level using eqn (1) or eqn (2). From a number of PL imagestaken with different illumination intensities, the injection leveldependence of the bulk lifetime can thus be calculated and plotted for aspecific area or a single pixel.

For comparison, we now consider the influence of injection level onQSSPC data. An example QSSPC tool, the Sinton Consulting ‘boule tester’,reports bulk lifetime as a function of injection level. Line scans ofthe estimated bulk lifetime are reported at a constant average carrierdensity, commonly at Δn_(avg)=5*10¹⁴ cm⁻³. Since a broad band lightsource is used in this system, a simple analytical solution is notpossible. Assuming illumination with 1100 nm light (α=3.5 cm⁻¹) thecondition αL<1 is fulfilled for bulk lifetimes τ_(bulk)<3 ms, and inthis range the average injection level scales with the bulk lifetimeaccording to eqns (1) and (3), similar to the usual case of lifetimemeasurements on wafers. With 1 Sun equivalent illumination intensity(N_(s)=3*10¹⁷ cm⁻² s⁻¹) and α=3.5 cm⁻¹ we calculate Δn_(avg)=4.7*10¹²cm⁻³ and Δn_(avg)=3.7*10¹³ cm⁻³ for τ_(bulk)=10 μs and τ_(bulk)=100 μsrespectively according to eqn (1). To achieve the commonly reportedaverage carrier density of Δn_(avg)=5*10¹⁴ cm⁻³, an incident lightintensity of about 100 Suns (N_(s)=3*10¹⁹ cm⁻² s⁻¹) is thus required forτ_(bulk)=10 μs. Shorter lifetimes reported at Δn_(avg)=5*10¹⁴ cm⁻³ wouldrequire even larger light intensities. Note that these intensity factorsdepend strongly on the exact spectral content in the light intensityprofile, but these figures show that large light intensities aregenerally required in typical QSSPC measurements to achieveΔn_(avg)=5*10¹⁴ cm⁻³. These light intensities are unrealistic forconventional solar cell applications since solar cells are normallyoperated at one Sun equivalent illumination and at an operating pointthat reduces the carrier density inside the wafer to a value that wouldbe achieved at 0.05 Suns under open circuit conditions. Lifetime datareported for tens or hundreds of Suns therefore have only limitedrelevance for solar cell applications.

In the description provided herein, numerous specific details are setforth. However, it is understood that embodiments of the invention maybe practised without these specific details. In other instances,well-known methods, structures and techniques have not been shown indetail in order not to obscure an understanding of this description.

Although the present invention has been described with particularreference to certain preferred embodiments thereof, variations andmodifications of the present invention can be effected within the spiritand scope of the following claims.

1-39. (canceled)
 40. A method of conducting an analysis of asemiconductor material, said method including the steps of: (a) excitingsaid material to produce photoluminescence; (b) measuring the intensityof the photoluminescence emitted from said material; (c) normalising themeasured photoluminescence intensity with regard to variations in thebackground doping density of said material to obtain a normalisedphotoluminescence intensity; and (d) analysing said normalisedphotoluminescence intensity in terms of one or more properties of saidmaterial.
 41. A method according to claim 40, wherein a substantial areaof said material is excited, and said measuring step images thephotoluminescence emitted from said area.
 42. A method according toclaim 40, wherein said material is a silicon ingot or a silicon brickand wherein said method is applied to at least one side facet of saidingot or brick.
 43. A method according to claim 40, wherein saidbackground doping density is measured experimentally.
 44. A methodaccording to claim 40, wherein said background doping density isdetermined empirically or calculated using a theoretical relationship.45. A method according to claim 40, wherein said normalisedphotoluminescence intensity is interpreted as a measure of the effectiveminority carrier lifetime of said material.
 46. A method according toclaim 40, wherein said normalised photoluminescence intensity isconverted to a measure of the bulk minority carrier lifetime of saidmaterial using a predetermined theoretical relationship between bulklifetime and normalised photoluminescence intensity.
 47. A methodaccording to claim 46, wherein one said theoretical relationship isapplied to multiple samples of said material with similar surfacepreparation.
 48. A method according to claim 40, wherein said propertyis the area or volume density of dislocations in said material.
 49. Amethod according to claim 40, wherein the photoluminescence measurementsare used as a cutting guide in wafer production.
 50. A method accordingto claim 40, wherein the information obtained from said method is usedto improve the manufacturing of silicon bricks or ingots.
 51. A methodaccording to claim 40, wherein the information obtained from said methodis used to determine the price of wafers derived from said material. 52.A method according to claim 40, wherein the photoluminescencemeasurements are used as a guide in wafer production to sort wafers intoquality bins.
 53. A method according to claim 40, wherein theinformation obtained from said method is used to obtain feedback onfeedstock quality in the production of silicon wafers.
 54. A system forconducting an analysis of a semiconductor material, said systemincluding: a photodetection unit for obtaining at least one image orline scan of photoluminescence generated from a surface of saidmaterial; and a processor for normalising the measured photoluminescenceintensity with regard to variations in the background doping densityacross said surface, and for analysing the normalised photoluminescenceintensity in terms of one or more properties of said material.
 55. Asystem according to claim 54, further including: an optical sourceemitting light with wavelength longer than the band-gap of silicon or ofsaid semiconductor material; and a detector for measuring thetransmission of said light through said silicon or semiconductormaterial.
 56. A system according to claim 54, wherein saidphotodetection unit includes an InGaAs camera.
 57. A system according toclaim 54, wherein said photodetection unit includes a silicon camera.58. A system when used to implement the method according to claim 40.59. A method of conducting an analysis of a semiconductor material, saidmethod including the steps of: (a) exciting a portion of said materialto produce photoluminescence; (b) measuring the distribution of thephotoluminescence emitted from said portion; (c) normalising themeasured photoluminescence distribution with regard to variations in theeffective minority carrier lifetime across said portion; and (c)analysing the normalised photoluminescence distribution in terms ofvariations in the background doping density of said material across saidportion.
 60. A method according to claim 59, wherein said material is asilicon ingot or a silicon brick and wherein said method is applied toat least one side facet of said ingot or brick.
 61. A method accordingto claim 59, wherein said portion is in the form of a line scan or atwo-dimensional area.
 62. A method according to claim 59, wherein saidmethod is applied to an ingot, brick or wafer of upgraded metallurgicalgrade silicon.
 63. A method according to claim 62, wherein the positionof a minimum in the distribution of said photoluminescence is fitted toobtain the ratio of donor and acceptor concentrations in the feedstockof said upgraded metallurgical grade silicon.
 64. A method according toclaim 59, wherein the photoluminescence measurements are used as acutting guide in wafer production.
 65. A method according to claim 59,wherein the information obtained from said method is used to improve themanufacturing of silicon bricks or ingots.
 66. A method according toclaim 59, wherein the information obtained from said method is used todetermine the price of wafers derived from said material.
 67. A methodaccording to claim 59, wherein the photoluminescence measurements areused as a guide in wafer production to sort wafers into quality bins.68. A method according to claim 59, wherein the information obtainedfrom said method is used to obtain feedback on feedstock quality in theproduction of silicon wafers.
 69. A system for conducting an analysis ofa semiconductor material, said system including: a photodetection unitfor obtaining at least one image or line scan of photoluminescencegenerated from a surface of said material; and a processor fornormalising the measured photoluminescence intensity in each part ofsaid image or line scan with regard to variations in the effectiveminority carrier lifetime across said surface, and for analysing thenormalised photoluminescence image or line scan in terms of variationsin the background doping density across said surface.
 70. A systemaccording to claim 69, further including: an optical source emittinglight with wavelength longer than the band-gap of silicon or of saidsemiconductor material; and a detector for measuring the transmission ofsaid light through said silicon or semiconductor material.
 71. A systemaccording to claim 69, wherein said photodetection unit includes anInGaAs camera.
 72. A system according to claim 69, wherein saidphotodetection unit includes a silicon camera.
 73. A system when used toimplement the method according to claim
 59. 74. A method of conductingan analysis of a semiconductor material, said method including the stepsof: (a) exciting a portion of said material to producephotoluminescence; (b) measuring the distribution of thephotoluminescence emitted from said portion; and (c) analysing thephotoluminescence distribution in terms of variations in the backgrounddoping density of said material across said portion.
 75. A methodaccording to claim 74, wherein the position of a minimum in saidphotoluminescence distribution is used to identify the position of atransition region from p-type to n-type in upgraded metallurgical gradesilicon.
 76. A method according to claim 74, wherein thephotoluminescence measurements are used as a cutting guide in waferproduction.
 77. A method according to claim 74, wherein the informationobtained from said method is used to improve the manufacturing ofsilicon bricks or ingots.
 78. A method according to claim 74, whereinthe information obtained from said method is used to determine the priceof wafers derived from said material.
 79. A method according to claim74, wherein the photoluminescence measurements are used as a guide inwafer production to sort wafers into quality bins.
 80. A methodaccording to claim 74, wherein the information obtained from said methodis used to obtain feedback on feedstock quality in the production ofsilicon wafers.
 81. A system when used to implement the method accordingto claim 74.